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On the approximate controllability for some explosive parabolic problems


Díaz Díaz, Jesús Ildefonso and Lions, J.L. (1999) On the approximate controllability for some explosive parabolic problems. In Optimal control of partial differential equations. International Series of Numerical Mathematics (133). Birkhäuser Verlag AG, Basel, pp. 115-132. ISBN 3-7643-6151-4

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We consider in this paper distributed systems governed by parabolic evolution equations which can blow up in finite time and which are controlled by initial conditions. We study here the following question : Can one choose the initial condition in such a way that the solution does not blow up before a given time T and which is, at time T, as close as we wish from a given state ? Some general results along these lines are presented here for semilinear second order parabolic equations as well as for a non local nonlinear problem. We also give some results proving that "the more the system will blow up" the "cheaper" it will be the control.

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International Conference on Optimal Control of Partial Differential Equations.CHEMNITZ, GERMANY . APR 20-25, 1998

Subjects:Sciences > Mathematics > Differential geometry
ID Code:15662

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